For the existence of polynomial solutions of Heun equation, one of the parameters \( \alpha \)  or \( \beta \)  must be chosen conveniently. For instance, for the class VIII Heun polynomial these parameters are chosen to be \( \alpha =\epsilon +\gamma +\delta -n-3 \)  and \( \beta = n+2\)  [1]}. In the solution which is obtained by extended NU method, the parameters \( \alpha \)  and \( \beta \)  can be determined exactly. Also the accessory parameter \(q\)  is specified exactly up to a constant of integration.
